(5 pt., 2.5 pt. each) Find the transitive closure of each of the following relations on the set 1,2,3,4 a. R={(1,1), (1,4), (2,1), (2,3), (3, 1), (3,2), (3,4), (4,2)). b. R = {(2, 1), (2,3), (3,1), (3,4), (4, 1), (4,3)). 3. 4. (10 pt., 5 pt. each) Draw a Hasse diagram for each of the following partial orders. Find the maximal and minimal elements and determine whether the partial order is a total order. R is a partial order on the set 12, 3,5,10,11,15,25) such that (x, y) E R if and only if x divides y. a. b. R is a partial order on the set (0, 1,2,3, 4, 5) such that (x, y) e R if and only if x 2 y